#include <vector>
#include <numeric>
#include <algorithm>
#include <random>
#include <cmath>
#include <set>
// Declare the interactor
long long collisions(std::vector<long long> x);
namespace {
// Helper to find divisors of difference
std::vector<long long> get_divisors(long long val) {
std::vector<long long> divs;
for (long long i = 1; i * i <= val; ++i) {
if (val % i == 0) {
divs.push_back(i);
if (val / i != i) divs.push_back(val / i);
}
}
std::sort(divs.begin(), divs.end());
return divs;
}
// Verify candidate N (Cost: 2)
bool check_n(long long n) {
if (n <= 0) return false;
std::vector<long long> q = {1, n + 1};
return collisions(q) > 0;
}
// Standard Divide & Conquer to isolate a colliding pair
// Guaranteed to terminate because the input set has collisions.
int solve_collision(std::vector<long long>& current_set, long long min_n, std::mt19937_64& rng) {
while (true) {
// Optimization: If set is small, brute force differences
if (current_set.size() <= 24) {
for (size_t i = 0; i < current_set.size(); ++i) {
for (size_t j = i + 1; j < current_set.size(); ++j) {
long long diff = std::abs(current_set[i] - current_set[j]);
if (diff < min_n) continue; // Skip if we know N is larger
// Check divisors of the difference
std::vector<long long> cands = get_divisors(diff);
for (long long cand : cands) {
if (cand < min_n) continue;
if (check_n(cand)) return (int)cand;
}
}
}
break; // Should not happen if collision exists
}
// Split
int sz = current_set.size();
int mid = sz / 2;
std::vector<long long> left_part(current_set.begin(), current_set.begin() + mid);
std::vector<long long> right_part(current_set.begin() + mid, current_set.end());
// Check Left
if (collisions(left_part) > 0) {
current_set = left_part;
}
// Check Right
else if (collisions(right_part) > 0) {
current_set = right_part;
}
// Crossing Collision
else {
// Must shuffle to create a new random split
std::shuffle(current_set.begin(), current_set.end(), rng);
}
}
return -1;
}
}
int hack() {
std::mt19937_64 rng(1337);
// --- Phase 1: Deterministic Check for Small N (<= 1,000,000) ---
// Construction: {1..B} U {B, 2B... B*B} with B=1000
// Covers all differences up to 1,000,000.
// Cost: ~2000.
{
const long long B = 1000;
std::vector<long long> small_set;
small_set.reserve(2 * B + 5);
for (long long i = 1; i <= B; ++i) small_set.push_back(i);
for (long long i = 1; i <= B; ++i) small_set.push_back(i * B);
// Ensure distinctness
std::sort(small_set.begin(), small_set.end());
small_set.erase(std::unique(small_set.begin(), small_set.end()), small_set.end());
if (collisions(small_set) > 0) {
// N is small. Isolate it.
return solve_collision(small_set, 1, rng);
}
}
// --- Phase 2: Deterministic Check for Large N (up to 10^9) ---
// Construction: {1..K} U {K, 2K... K*K} with K=32000
// Covers all differences up to ~1.024 * 10^9.
// Set Size: ~64,000.
{
const long long K = 32000;
std::vector<long long> large_set;
large_set.reserve(2 * K + 5);
// Part A: {1, ..., K}
for (long long i = 1; i <= K; ++i) large_set.push_back(i);
// Part B: {K, 2K, ..., K*K}
// Note: We go up to K*K + some buffer if needed, but K*K > 10^9 is enough.
// K*K = 1,024,000,000.
for (long long i = 1; i <= K; ++i) large_set.push_back(i * K);
std::sort(large_set.begin(), large_set.end());
large_set.erase(std::unique(large_set.begin(), large_set.end()), large_set.end());
// This query guarantees a collision if N <= 10^9
if (collisions(large_set) > 0) {
// We know N > 1,000,000 from Phase 1, so we can pass that as min_n
// to speed up the brute-force check at the leaf nodes.
return solve_collision(large_set, 1000000, rng);
}
}
// Fallback (should never be reached for N <= 10^9)
return -1;
}
